New Jersey Democrat Sen. Cory Booker said he would support the Iran nuclear accord on Thursday, splitting with his state’s senior senator over the contentious deal. […]

Also on Thursday, Democratic Sens. Mark Warner of Virginia and Heidi Heitkamp of North Dakota backed the Iran agreement, bringing support for the deal up to 37 senators.

Arguably no member of Congress in either chamber faced as much pressure as Booker, with many of his key backers pushing him – aggressively – to oppose the U.S. policy. The fact that he bucked the pressure is worthy of real praise; it couldn’t have been easy for him to do the right thing.

As for the larger context, remember, the magic number was 34 – with 34 votes in the Senate, the White House is assured that the policy will advance because Congress won’t have the votes to override a presidential veto.

Now proponents of the diplomatic agreement have a new threshold in mind: 41.

Remember, we know how the process is likely to unfold: the bill to kill the diplomatic solution will pass the House, and will then go to the Senate. In the upper chamber, it’s long been assumed that the legislation would clear the Senate with relative ease, then face President Obama’s veto, and then return to the Hill for a veto-override showdown.

But as support for the deal grows, the expectations are shifting. Assuming Senate Democrats filibuster the kill-the-deal measure, Republicans will need 60 votes just to get the bill to the Oval Office. It’s starting to look like those votes may not materialize.

There are only seven Democrats remaining who have not yet announced their position: Michael Bennet (Colo.), Richard Blumenthal (Conn.), Maria Cantwell (Wash.), Ben Cardin (Md.), Joe Manchin (W.Va.), Gary Peters (Mich.), and Ron Wyden (Ore.). How many are prepared to partner with the far-right, even knowing the proposal is doomed? Watch this space.

At the risk of making this needlessly complicated, there is just one additional angle I want to put on readers’ radar: some Dems who support the deal may not support a filibuster. Manchin, in particular, appears to fall into this camp.

I mention this because it’s not, strictly speaking, a matter of counting heads. It’s possible, if not likely, that there will be at least 41 Senate Democrats supporting the policy, but that doesn’t necessarily mean there will be 41 votes for blocking the bill. How they vote on the process and legislative procedures matters.

But for now, let’s not get bogged down in these details. The key takeaway today is that three more senators announced their position on the agreement today, and each of them support the deal. Far-right critics who were confident of success are left to wonder what went wrong.